Long story short, the military wasn't happy with PALs being put on nuclear weapons. PALs are designed to ensure a nuclear weapon cannot be detonated without command authorization. So, it's a lockout. This is nice, if everything works as it should and there's no communication issues. The military wanted its weapons to work even under the worst of circumstances. So the "launch codes" were set to all zeros to ensure the weapons could be launched if the Soviets decided to go with a first strike instead of sitting around doing nothing because everyone with the codes is dead or out of communication.
These are not the codes that the President has in the football that gets carried around. Those are authentication codes, and they can't be used to directly launch a nuclear weapon. I know this is contrary to every bad movie made involving nuclear launch codes. They authenticate the President as being the President, and that his orders are verified.
Even with the PAL lockouts being set to all zero, you needed a number of people intentionally working together to launch an armed nuclear weapon.
OTOH, it'd be pretty much easier to manufacture a new nuclear weapon than try to hotwire an existing nuclear weapon to detonate without the PAL codes.